Question 239345: A father is 3 times as old as his son, after 15 years, the father will be twice as old as his son at that time, therefore, the fathers current age is:
4, 8, 16, 32 or 64
How is this worked out please?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! With these age problems, start by writing an expression for each person's age at each point in time mentioned in the problem. In your problem you have two people (father and son) and two points in time (now and 15 years in the future). So we will want 4 expressions of age.
When writing expressions I recommend that you make the variable represent the smallest unknown number (if you know what the smallest one will be). This allows you to use addition and/or multiplication to express some or all of the other unknown numbers.
In your problem, the son's current age is the smallest number so:
Let x = the son's current age
then 3x = the father's current age
and x+15 = the son's age in 15 years
and 3x+15 = the father's age in 15 years.
After we write the expressions we need to write equation(s). We need as many equations as the number of variables we've used. Since we were able to write all 4 expressions with just one variable, we will only need one equation. And we will write this equation using the only relationship we have not used already: "after 15 years, the father will be twice as old as his son at that time". In other words: The father's age in 15 years will be twice the son's age in 15 years. Using our expressions from above this sentence translates into:
3x + 15 = 2(x+15)
Once we have our equation(s) we solve them. Our equation is a fairly simple one to solve.
Simplify.
3x + 15 = 2x + 30
Subtract 2x from each side
x + 15 = 30
Subtract 15 from each side
x = 15
We can now use this solution to the equation and our expressions to answer the question: "The father's current age is ...". Since the expression for the father's current age was 3x, the answer is 3(15) = 45
As we can see, 45 is 3 times 15 and, in 15 years, 45+15 is the same as 2(15+15) so these numbers are correct.
I don't why 4, 5, 16, 32 or 64 are listed as possible solutions. In fact none of these numbers could have possibly been the answer since none of them is a multiple of 3 and the father's age would have to be a multiple of 3 since it is 3 times the son's age.
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